Does restricting access to alcohol reduce traffic accidents? Not necessarily, according to a recent study by economists from the University of Lancaster: 

Recent legislation liberalised closing times with the object of reducing social problems thought associated with drinking to “beat the clock.” Indeed, we show that one consequence of this liberalization was a decrease in traffic accidents. This decrease is concentrated heavily among younger drivers. Moreover, we provide evidence that the effect was most pronounced in the hours of the week directly affected by the liberalization; late nights and early mornings on weekends.

The authors also suggest that the restrictive closing times caused more traffic congestion (everyone left the pubs at the same time), increasing the scope for accidents.

So more freedom seems to generate better outcomes, presumably because most people use increased freedom sensibly.